Momentum exerted to a lateral wall of a helicon plasma source is individually measured for argon, krypton, and xenon gases. A significant loss of the axial plasma momentum to the lateral wall, which has been assumed to be negligible, is experimentally identified when an axially asymmetric density profile is formed in the source. This indicates that the radially lost ions deliver not only the radial momentum but also the axial momentum to the lateral wall. The formation of the axial asymmetry causing the momentum loss is interpreted with competition between the magnetic field and neutral depletion effects.